The interface of noncommutative geometry and physics
As a mathematical theory per se, noncommutative geometry (NCG) is by now well established. From the beginning, its progress has been crucially influenced by quantum physics: we briefly review this development in recent years. The Standard Model of fundamental interactions, with its central role for...
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| Tipo de documento: | capítulo de livro |
| Data de publicação: | 2004 |
| País: | Costa Rica |
| Recursos: | Universidad de Costa Rica |
| Repositório: | Kérwá |
| Idioma: | inglês |
| OAI Identifier: | oai:kerwa.ucr.ac.cr:10669/88500 |
| Acesso em linha: | https://link.springer.com/chapter/10.1007/978-1-4612-2044-2_15 https://hdl.handle.net/10669/88500 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Geometría no conmutativa Algebra de Hopf Modelo Estándar de interacciones fundamentales MATEMÁTICAS |
| Resumo: | As a mathematical theory per se, noncommutative geometry (NCG) is by now well established. From the beginning, its progress has been crucially influenced by quantum physics: we briefly review this development in recent years. The Standard Model of fundamental interactions, with its central role for the Dirac operator, led to several formulations culminating in the concept of a real spectral triple. String theory then came into contact with NCG, leading to an emphasis on Moyal-like algebras and formulations of quantum field theory on noncommutative spaces. Hopf algebras have yielded an unexpected link between the noncommutative geometry of foliations and perturbative quantum field theory. The quest for a suitable foundation of quantum gravity continues to promote fruitful ideas, among them the spectral action principle and the search for a better understanding of "noncommutative spaces". |
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